Structural Seismic Reliability Analysis

Perhaps, no other discipline within engineering has to deal with as much uncertainty as the field of earthquake engineering (Der Kiureghian 1996). To begin with, the occurrence of earthquakes in time and space is completely random in nature, and this leads to a large amount of uncertainty while predicting the intensities of ground motions resulting from earthquakes. Further, it is challenging to precisely assess the load-carrying capacity of the structural system of interest, due to the inherent variability across different structural members that constitute the overall structural system. It is necessary to analyze all of these different sources of uncertainty and assess the safety of the structure by accounting for such sources of uncertainty. Structural safety assessment is important both during the design of the structural system and for analyzing its performance while the system is under operation, particularly before and after earthquakes. Engineering design is usually a trade-off between maximizing safety levels and minimizing cost. It is necessary to account for the uncertainty in anticipated loading conditions and the different sources of uncertainty regarding the structural system while assessing safety during system design. Traditional design approaches simplify the problem by treating the uncertain quantities to be deterministic and account for the inherent uncertainty through the use of empirical safety factors, also referred to as deterministic safety factors. These empirical safety factors do not provide any information on how the different uncertain quantities influence the overall structural safety. Therefore, it is difficult to design a system with a uniform distribution of safety levels among the different components using empirical safety factors (Haldar andMahadevan 2000). Further, during the design stage, deterministic safety factors do not provide adequate information to achieve optimal use of the available resources to maximize safety. For these reasons, it is necessary to use probabilistic approaches that rigorously account for the different sources of uncertainty and directly aid in the design of the structural system. Probabilistic approaches directly calculate the probability that the structural system may fail by probabilistically analyzing the load-carrying capacity of the structure and the actual loading on the structure. The safety of the structure is defined in terms of the converse of the probability of failure, which in turn is used to compute the so-called reliability metric that measures the probabilistic reliability of the structure. In fact, probabilistic methods provide a systematic framework to analyze the different sources of uncertainty, quantify their individual contributions to the overall structural safety, and aid in efficient design by choosing design parameters that maximize the reliability of the structure.